Q55 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is defined as \(f(x)=\frac{x^6}{x^6+2020}\), \(\forall x \in \mathbf{R}\), then the range of \(f\) is .......

  • A
    \([0,1]\)
  • B
    \([0, \infty)\)
  • Correct answer
    C
    \([0,1)\)
  • D
    \(\left[0, \frac{1}{2020}\right)\)

Solution

We have, \(\begin{aligned} & \quad x^6+2020 > x^6 \\ & \Rightarrow \frac{x^6}{x^6+2020} < 1 \\ & \therefore \text { Range }=[0,1) \end{aligned}\) Hence, option (c) is correct.

Hence, the correct answer is option: 'C'.

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